18.5. Rotation Operations

Try these first

1. 1.

   What defines the slope of a node in a binary tree?

   Hint

   Think about how we measure heights of separate subtrees.

2. 2.

   What is performed when the slope is +2?

   Hint

   Consider what happens based on left properties.

3. 3.

   What happens when the slope of a node is +2?

   • Left Rotation
   • Right Rotation
   • No Rotation

   Hint

   Think about how we correct balance favoring the left subtree.

4. 4.

   True or False: Heights must be computed recursively for every tree operation.

   • True
   • False

   Hint

   Remember why it's inefficient to compute heights all the time.

5. 5.

   In a binary tree with a series of insertions leading to an imbalance, describe how you would perform successive right and left rotations.

   Hint

   Map out the tree after several insertions to visualize needed rotations.

6. 6.

   Explain the consequences of failing to maintain height information in nodes after rotations.

   Hint

   Consider how balancing impacts retrieval performance.